Question: Astrid is in charge of building a new fleet of ships. Each ship requires $40$ tons of wood, and accommodates $300$ sailors. She receives a delivery of $4$ tons of wood each day. The deliveries can continue for $100$ days at most, afterwards the weather is too bad to allow them. Overall, she wants to build enough ships to accommodate at least $2100$ sailors. How much wood does Astrid need to accommodate $2100$ sailors?
There can be many ways to solve this problem. Here, we will do this by thinking about units. Let's say that Astrid needs $x\,\text{tons}$ of wood to accommodate $2100\,\text{sailors}$. How can we relate these two quantities with an equation? $\begin{aligned} x\,\text{tons}\cdot y\,\dfrac{\text{sailors}}{\text{ton}}=2100\,\text{sailors} \end{aligned}$ So in order to find the amount of wood $x$, we need to figure out the value of $y$, which is the rate of sailors per ton of wood. Notice what other information we are given: $40\,\dfrac{\text{tons}}{\text{ship}}$ $300\,\dfrac{\text{sailors}}{\text{ship}}$ $4\,\dfrac{\text{tons}}{\text{day}}$ $100\,\text{days}$ Which of these quantities can help us calculate a rate whose units are $\dfrac{\text{sailors}}{\text{ton}}$ ? We can combine the following quantities: $\begin{aligned} &\phantom{=}\dfrac{300\,\dfrac{\text{sailors}}{\text{ship}}}{40\,\dfrac{\text{tons}}{\text{ship}}} \\\\ &=\dfrac{300}{40}\,\dfrac{\text{sailors}}{\cancel\text{ship}}\cdot\dfrac{\cancel\text{ships}}{\text{ton}} \\\\ &=7.5\,\dfrac{\text{sailors}}{\text{ton}} \end{aligned}$ Now we can plug that in the original equation: $\begin{aligned} x\,\text{tons}\cdot 7.5\,\dfrac{\text{sailors}}{\text{ton}}&=2100\,\text{sailors} \\\\ x\,\text{tons}&=\dfrac{2100}{7.5}\,\cancel\text{sailors}\cdot\dfrac{\text{tons}}{\cancel\text{sailor}} \\\\ x\,\text{tons}&=280\,\text{tons} \end{aligned}$ In conclusion, to accommodate $2100$ sailors, Astrid needs $280$ tons of wood.